Problem: Express your answer as a mixed number simplified to lowest terms. $5\dfrac{1}{5}-1\dfrac{4}{10} = {?}$
Explanation: Simplify each fraction. $= {5\dfrac{1}{5}} - {1\dfrac{2}{5}}$ Find a common denominator for the fractions: $= {5\dfrac{1}{5}}-{1\dfrac{2}{5}}$ Convert ${5\dfrac{1}{5}}$ to ${4 + \dfrac{5}{5} + \dfrac{1}{5}}$ So the problem becomes: ${4\dfrac{6}{5}}-{1\dfrac{2}{5}}$ Separate the whole numbers from the fractional parts: $= {4} + {\dfrac{6}{5}} - {1} - {\dfrac{2}{5}}$ Bring the whole numbers together and the fractions together: $= {4} - {1} + {\dfrac{6}{5}} - {\dfrac{2}{5}}$ Subtract the whole numbers: $=3 + {\dfrac{6}{5}} - {\dfrac{2}{5}}$ Subtract the fractions: $= 3+\dfrac{4}{5}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{4}{5}$